Related papers: Consistent adjacency-spectral partitioning for the…
Graph-based semi-supervised learning is one of the most popular methods in machine learning. Some of its theoretical properties such as bounds for the generalization error and the convergence of the graph Laplacian regularizer have been…
We argue that existing training-free segmentation methods rely on an implicit and limiting assumption, that segmentation is a spectral graph partitioning problem over diffusion-derived affinities. Such approaches, based on global graph…
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general…
Random graphs have been widely used in statistics, for example in network analysis and graphical models. In some applications, the data may contain an inherent hierarchical ordering among its vertices, which prevents directed edges between…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Semi-supervised semantic segmentation requires the model to effectively propagate the label information from limited annotated images to unlabeled ones. A challenge for such a per-pixel prediction task is the large intra-class variation,…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
This article considers spectral community detection in the regime of sparse networks with heterogeneous degree distributions, for which we devise an algorithm to efficiently retrieve communities. Specifically, we demonstrate that a…
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Spectral analysis has been successfully applied at the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix,…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein \emph{et al.} \emph{Phys. Rev. A,} \textbf{73}:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
The two-step spectral clustering method, which consists of the Laplacian eigenmap and a rounding step, is a widely used method for graph partitioning. It can be seen as a natural relaxation to the NP-hard minimum ratio cut problem. In this…
Multilayer networks generalize single-layered connectivity data in several directions. These generalizations include, among others, settings where multiple types of edges are observed among the same set of nodes (edge-colored networks) or…
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its…
The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…
Suppose that a graph is realized from a stochastic block model where one of the blocks is of interest, but many or all of the vertices' block labels are unobserved. The task is to order the vertices with unobserved block labels into a…
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the…